Well, in Mathematics there are somethings, which appear true but they aren't true. Naive students often get fooled by these results.

Let me consider a very simple example. As a child one learns this formula $$(a+b)^{2} =a^{2}+ 2 \cdot a \cdot b + b^{2}$$ But as one mature's he applies this same formula for Matrices. That is given any two $n \times n$ square matrices, one believes that this result is true: $$(A+B)^{2} = A^{2} + 2 \cdot A \cdot B +B^{2}$$ But eventually this is false as Matrices aren't necessarily commutative.

I would like to know whether there any such things happening with physics students as well. My motivation came from the following MO thread, which many of you might take a look into:

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@MArek: i didnt find the option. if anyone can do it they are welcome
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S.C.Nov 17 '10 at 23:15

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@Chandru: AFAIK StackExchange recently changed its rules about this matter so that only moderators can make a question community wiki (the rationale being that the CW option is being misused at StackOverflow).
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MarekNov 17 '10 at 23:26

22

While i perceive the question interesting, I think the example with matrices is rather 'a common silly mistake' than 'a common false belief'.
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Piotr MigdalNov 17 '10 at 23:48

6

It seems a bit odd to be accepting a single answer to a soft question...
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David Z♦Dec 1 '10 at 0:21

49 Answers
49

It's a common false belief among cynical physicists that there is no physical meaning in asking "why is there something rather than nothing". The question of whether there is an inevitable, self-consistent, self-referencial mathematical law that mandates the universe to exist is a real and legitimate one, a unified theory would be a step in the right direction. Research in number theory, prime numbers, infinity, etc, also plays into this.

"Summer is when the Earth is closest to the sun, and winter is when it's furthest away."

It's true that the Earth's orbit is slightly elliptical, but the effect of this, as far as seasons, is very small. For one thing, this wouldn't explain why the sun rises and sets at different times in different seasons, and if this were true, the whole planet would have summer at the same time.

The seasons are actually caused by the tilt of the Earth relative to its orbit around the Sun.

A mistake that I often come across and that is so easy to make: people somehow have a visceral belief that heavy objects fall faster than light ones. Setting aside of course problems of air resistance, this is obviously false, but it seems to be so counterintuitive and I think it is somehow tied to our intuitive understanding of mass as inertia. Since higher mass means higher inertia. People understand this intuitively as it takes more force to push a fat guy than a thin one. But they don't see that gravity is a force proportional to mass, so that more inertia is paralleled by more gravity as well. With as a result the same gravitational acceleration for light and heavy bodies.

I've even noticed the mistake being made by professional physicists in colloquial conversations.

EDIT: I just found this article today, shedding a new light on why misconceptions in physics or science in general are so common and so hard to get rid of.

+1 for "setting aside air resistance"... it always bugs me when people point out how things fall at the same rate, while neglecting to mention that this assumes air resistance is negligible. Leaving out this clarification I think leads to more confusion, as all someone has to do is drop a rock next to a feather to (incorrectly) conclude that Galileo was wrong.
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Tim GoodmanNov 18 '10 at 3:22

8

If you are assuming a fixed earth, then you are correct. But if you let the earth move, then the Earth moves more rapidly when you drop a bigger mass than when you drop a smaller one. In that sense, bigger masses drop faster. This has nothing to do with the equivalence principle of course.
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VagelfordNov 18 '10 at 17:49

7

Seems important to mention here Galileo's famous gedankenexperiment. If you follow the line of thought that heavy objects fall faster, and go split a heavy falling object in two, large one and big one, both should be falling slower than the original. The upper part would be pulling lower part up, wanting to go even slower, hence a contradiction.
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Pavel RadzivilovskyDec 1 '10 at 9:44

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There is also the complication of buoyancy - a dense object would be heavier at the same mass, and thus fall faster even if air was friction-less.
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romkynsJan 12 '11 at 1:22

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@Pavel You're ignoring tidal effects. Splitting something in two doesn't really change anything, because the two halves, being in close proximity, experience different tidal forces than those between two objects farther apart.
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ErikEJan 21 '11 at 18:21

Here's another list of false beliefs. These are held by science popularizers. Whether they actually believe these beliefs, or just utter them for the purpose of getting more viewers, is an unanswerable question:

The curved space near massive object can be pictured as a deformed rubber sheet

This one is due to Einstein, unfortunately. You put balls on a rubber sheet, and you see that they roll towards each other. The reason this is a terrible explanation is because you have the Earth's gravity doing the pulling, not the curved space. The actual geodesics on a curved space like the rubber sheet are repelled by the central mass. The reason things attract in relativity is because of the time-dilation factor, and this is the dominant effect. It is just as easy to explain things correctly, in terms of time slowing down near a massive object, and world-lines trying to maximize their proper time with given fixed endpoints, but popularizers never do this.

A variable speed of light can replace inflation.

This appeared in a recent popular show, and it is based on the following bogus idea: if light moved faster at early times, then all the universe could have been in communication! The reason this is false is because no matter how the speed of light is imagined to vary, one can recoordinatize space-time in terms of the intersections of light cones, and unless these lightcones split instead of merge, you get the same communication paradox--- new regions coming into causal contact are coming into causal contact for the first time.

Mesons and Baryons are made of quarks like atoms are made of protons, neutrons and electrons.

This is insidious, because its true for heavy mesons. But it's much more false than true for pions and protons and all the excitations at lower than 1GeV, because of the vacuum condensates. There is no reasonable model of light pions which does not take into account their Goldstone nature. This type of explanation also leaves out Nambu and Skyrme, both of whom were unjustly ignored for too long.

String theory is a theory of strings

This picture is not good for someone who doesn't already have a sense of string theory, because if you start out making home-made models of relativistic strings, you will never get anything like the correct string theory. The strings you naively picture would not have the special light-cone interactions that strings do in the Mandelstam picture, and they would not obey Dolen Horn Schmidt duality. They would just be conglomerations of point particles held together by rubber bands. They would have the wrong spectrum, and they would be full of ghosts.

The only proper way to say what strings are is to say right off the bat that they are S-matrix states, and that they are designed to be an S-matrix theory with linear Regge trajectories. They have a string picture, but the constraint that exchanging strings in the S-channel is dual to exchanging them in the T-channel is all-important, just as it was all-important historically. Without this, even with the Nambu action, you are at a loss for how to incorporate interactions. It is not obvious that the interactions are by topology unless you know Dolan Horn Schmidt.

It is also important for realizing that string interactions are somewhat holistic (that they become local on the light cone is the surprise, not the other way around). You add them order by order in perturbation theory by demanding unitarity, not by asking what happens when two strings collide in the usual sense. These "strings" are strange new things born of 1960s Chew-isms, and their closest cousins are flux lines in gauge theory, or fishnet Feynman diagrams, not a collection of point masses held together by spring-like forces.

This is also insidious, because Chew, Mandelstam, Dolen, Scherk, and all that generation developed the greatest physical theory the world will ever see, and their reward was: "You're fired". (in Scherk's case, "You're crazy"). Then they were heckled for thirty years, while their work was appropriated by a new generation, who described them as the deluded misguided Chew-ites who discovered something great by accident.

There is more than a snowball's chance in hell for large extra dimensions

The idea that there are large extra dimensions was very popular in 2000, but it's completely preposterous. Large extra dimensions bring the planck mass down to about a TeV, giving neutrinos generic majorana masses which are in the KeV-MeV range, so you need to fine tune. They lead to essentially instantaneous proton decay, and huge CP violations in strong interactions, so you need to fine tune some more. To avoid proton decay, there is a clever mechanism due to Arkani-Hamed and Schmalz which puts the quarks and leptons in different places in the extra dimensions. This idea is appealing only at a superficial first glance, because it requires that the SU(2) and U(1) of the standard model be extended in the extra dimensions, which affects their running immediately. The theory predicts unambiguously and model-independently that proton decay suppression requires huge electroweak running at around a TeV. That's a signal you haven't seen a hint of at 100GeV collisions. Come on. In addition, how do you stabilize large dimensions? It's the same fine-tuning as before, so the number of problems has gone up.

A low Planck scale would completely demolish the predictivity of string theory. You can squeeze a lot of stuff into large dimensions. In my opinion, it is this brand of string theory that the critics correctly criticize as fundamentally non-predictive.

This is also a misconception of science in general, but I've heard many people say, "Physics (science) has proven. . ." or "Can we use Physics (science) to prove this?" The misconception is that the scientific method can prove something with 100% certainty. This is certainly not the case; experiments only validate a law in settings similar to that in which the experiments were conducted. Granted, we can often reasonably generalize our results far beyond particular settings, but we can only hold laws with certainty where they have been tested and verified.

Earth revolves around the Sun. It is wrong to say that the Sun revolves around the Earth.

FACT: Motion is relative. There is nothing wrong in saying the Sun revolves around the Earth. The former is more frequently mentioned because the Sun (or more accurately, barycenter) is a better inertial frame, and other planets revolve in a near circle around the Sun as well, but in a bizarre way around the Earth.

By traveling faster than light in the vacuum one can go back to the past.

Misconception - The uncertainty principle is a statement about "our" ability to make measurements.

Correction - The uncertainty principle is a result of the nature of the particles themselves and refers to the ability of anything to "make the relevant measurements". It's not just us that can't determine the simultaneous values of incompatable observables, God can't either.

I will give some meta-false beliefs: these are beliefs held by the general public, which happen to be true, which are hyper-corrected by many physicists with bogus corrections based on the urge to appear smart:

Electrons move slowly down a wire

The belief: the electrons move lightning fast down a wire.

the hypercorrection: in the completely obsolete Drude model, electrons move slowly. In this model, you imagine the current is carried by a classical gas of electrons, and you divide the total current by the density of all electronic charge to get the drift velocity. This predicts a completely bogus drift velocity of a few cm/s, which is total nonsense, because only electrons near the Fermi surface contribute to the conductivity. Nevertheless, you see this hypercorrection repeated endlessly (it appears here too).

The best answer: the electronic wavefunctions are spread out in a metal. The correct notion of electron velocity is the Fermi velocity, which is enormous typically, because the wavelength is about 1 atomic radius. While it isn't the same as the speed of electricity going down the wire (which is the speed of the field perturbations, some significant fraction of the speed of light), it is enormously high. Impurities which can scatter electrons will alter this speed, but not as much as the naive hypercorrection says.

The atom is mostly empty space

The belief: the atom is full of stuff, that's why stuff is hard when you push against it.

The hypercorrection: In the totally obsolete Rutherford-Bohr model, the atom is mostly empty space, the tiny pointlike electron orbiting a nucleus which contains most of the mass.

The best answer: But it is the electrons' wavefunction which tells you whether something is empty space or not. A region filled with electronic wavefunction feels hard to the touch, because two electrons can't be compressed into the same space without squeezing their wavefunction to have very high spatial variations, by the exclusion principle. Atoms are full of electronic wavefunction, and are therefore not empty space, at least not by any reasonable definition.

There is nothing mystical about measurement in quantum mechanics

The belief: the measurement problem in the standard quantum mechanics suggests that consciousness is somehow involved in measurements

hypercorrection: decoherence explains all that! Quantum mechanics is no different than determinism as far as enlightenment values are concerned.

The best answer: Decoherence tells you why you don't have interference between classically different worlds, or histories, and its an important part of the story if quantum mechanics is exact. But it does not tell you why you "percieve" one consistent history as a world. You need a dictionary between physics and perception. Since this dictionary is fundamental, and weird, and philosophical, it is important to explain that this is not an output of physics, but an input, which links mathematical theory with explicit sense-data.

There is no such thing as a centrifugal force

The belief: when things are rotating, they are pushed out by a centrifugal force.

The hypercorrection: There is no centrifugal force. There is a centripetal force (centripetal was a made up word to replace centrifugal) which pulls you in.

The best answer: This is obviously true from the point of view of the inertial frame, there is no centrifugal force, but if you are looking at it from the point of view of the rotating object, then there is. It all depends on your choice of reference frame.

The big bang happened everywhere at once

The belief: the big bang means that the universe started at some definite point and got bigger from there.

The hypercorrection: the big bang happened everywhere at once, and it is just wrong to think of it as happening at some single point in an extended model of space-time. If the universe is open, the big-bang was infinite in extent.

The best answer: There are three important caveats: 1. In FRW models, the bang-point is a singularity, so its outside space and time, and it is impossible to determine if it is "really" a single point or "really" everywhere at once, so it's just a meaningless question. 2. In the Newtonian "big bang" model, where you imagine the universe is now filled with particles which have a speed away from you linearly proportional to the distance from you, everything does come out from a single point! All the newtonian world lines converge on your current position. That's true even though the universe is spatially homogenous (the reason its not a paradox is that Galilean boosts are nontrivially mixed with translations). 3. the best picture, in my view, is the holographic picture, where you are surrounded by a horizon which was smaller in the past. This view is similar to the Newtonian big bang, in that everything came from a small region bounded by a dS cosmological horizon. This is mathematically equivalent to everything else, except throwing away the stuff outside the horizon that can't be observed.

I would like to admit that I was a little flabbergasted when a lay-person told me that everything in a Newtonian big-bang comes from a single place. That was completely counterintuitive.

Historically the concept of absolute velocity was commonly believed until the time of Galileo Galilei in the early 17th century. As a naive child, before studying basic physics, it is surprisingly easy to believe in this even these days!

The idea of absolute velocity states that all velocities are fixed with respect to an absolute frame of reference. Galileo showed that velocity is relative to your frame of reference, a principle known as Galilean relativity. This was later fully quantified by Isaac Newton, who also proposed that acceleration is invariant with respect to inertial frames.

I know it's an old question, but it's too much fun to pass this one up. There are quite a few examples of wrong ideas that have taken hold, but for the centrality to physics and the degree to which it is wrong and misleading, it is hard to find a better example than the Bohr atom. When it came out, it electrified the physics world on account of its revolutionary viewpoint and stunning success. But eleven years later it became completely obsolete. Nevertheless, in that short time it gripped the imagination of both the physics world and the general public to the point where it remains today the iconic picture of the atom in the minds of just about everyone.

The misleading influences of this model are extremely far reaching. One can begin with the idea of the "quantum leap", which begat wave function collapse, which begat multiple universes et cetera. But perhaps the most persistent holdover of the Bohr atom is the notion that the ordinary laws of electromagnetics must be suspended at the atomic level, otherwise the atom would be unstable. Of course, nothing of the sort is true in modern quantum mechanics, least of all for the hydrogen atom. The greatest triumph of the Schroedinger equation was to show that the motion of electric charge could be tracked through time, and that the stable atomic configurations were precisely those with no accelerating charge distributions. This was an immediate and obvious consequence of Schroedinger's solution for the hydrogen atom.

I would claim that it is not merely true that the stable configurations in QM are those with no accelerating charges. I would go further and suggest that in those cases where the charges do accelerate, the rate at which the kinetic energy of motion is converted into electromagnetic energy is exactly in agreement with that which would be calculated in the ordinary way by applying Maxwell's equations. So, for example, in the case of a black body radiator, if one simply takes the vibrating atoms, accounting for the accelerating motion of the charges, and applies classical antenna theory, you will get the correct black-body spectrum.

The concept that quantum mechanics undermines determinism. The Schrodinger wave equation evolution is completely deterministic. The results of measurements are probabilistic, but this does not mean that the various superposed states do not have causes. This is not the same thing as a hidden variable theory. The probabilities are deterministic.
T'Hooft has some interesting ideas on a determinism underlying QM (not the same thing as saying the wave equation is deterministic). I am not arguing that qm is in all senses deterministic, but it isn't completely non-deterministic either.

As an instructor, I have great difficulty teaching Newton's 3rd law: "For every action there's an opposite and equal reaction." This is very basic and very old physics but it's hard to teach. A typical example of the false reaction force answer is the following:

I hold an apple in my hand. The earth
pulls down on the apple with a
gravitational force. What is the
reaction force to this?

The answer most of them will give is that the reaction force is "my hand pushing up on the apple." Arggghhhh! Of course the reaction force is "the apple pulling up on the earth."

Students fail to realize that the opposite and equal reactions have to be between the same pair of objects. That is, forces arise as pairs. I wish they'd just rename the law so that it makes it more clear that the reaction force has to operate between the same pair of objects.

I demonstrate the law by holding a long spring in my hands and telling them that forces are like this spring. When it applies a force on one end it applies a force on the other (assume massless spring). Next quarter I'm going to try some more extreme measures on this, clearly I'm failing.

The misconceptions about special relativity and quantum mechanics are quite well-known. A lot of the posts above discuss them in detail. So rather than doing that I'll list some misconceptions from general(say high school) physics:

When a body rests on a surface the upward contact force acting on it is reaction to its weight. This is obviously wrong as action and reaction act on different bodies.

There's a lot of misconceptions about non-inertial(pseudo) force. My physics teacher once said that non-inertial forces arise only when the body is in contact with an accelerating frame.

Nothing can move faster than light. Of course it's false unless you add the phrase "in vacuum". The Cherenkov radiation happens when some charged particle moves in a medium with speed greater than the speed of light in that medium.

Friction always has to act in the opposite direction of overall motion. Actually friction provides the necessary force for rolling without which no vehicle would ever run. The correct formulation is friction opposes the instantaneous motion of the point of contact.

Light always travel in straight lines. Even without gravitational bending if we simply have a medium with a variable refractive index light will follow a curve through it. It's a nice application of Snell's law.

Newton's second law provides a definition of force. It's a very widespread misconception unfortunately even among professional physics students. This strips Newton's second law of any physical content and forces(pun intended) it to become a tautology. Of course the actual content of the law is that the force is given by some other law(say gravitational or em) and it equals ma. For a persuasive discussion on this see the first volume of Feynman's Lectures on Physics. (I am very sorry that I forgot the chapter or page number).

Newton's first law is derivable from second law. The proof goes as follows : F=ma. If F=0 then a=0 since $m~{}\neq 0$ QED. The problem is without first law there is no notion of an inertial frame and the laws become pointless.

In special relativity the hypothesis of the constancy of the speed of light in vacuum(c) with respect to all observers is redundant because it can be derived from the principle of relativity. Of course c may vary without contradicting the principle of relativity. In fact, in Newtonian mechanics c is observer dependent it respects the principle of relativity. The constancy of c hypothesis gives the Lorentz transformation whereas in Newtonian mechanics we have the Gallilean transformation. If you are still not convinced then look at this formulation of special relativity without the second hypothesis. Google doubly special relativity.

Also, I don't think anyone believes 5, 6 and 7 are arguable at best, and 8 is only stated by people who believe Maxwell's equations, so that the principle of relativity plus the validity of Maxwell's equations implies the constancy of the speed of light.
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Ron MaimonAug 16 '11 at 16:51

How about this - that parity is one of the most fundamental symmetries (which is not).

I know the experiment(s) showing parity violation. However, I guess what I still don't understand is the following, rotational symmetry is fundamental. And parity is just rotating 180 degrees. So if we say that all rotational symmetry is fundametal, why would a subset (rotating with a very specific angle - 180 degrees) not being fundamental? Isn't that self contradicting?

When a star collapses into a black hole, its gravitational pull does not actually increase.

Meteorites are not actually hot when they land; usually they are cold. (I would add: the heating of meteors is more due to the compression of the air in front of them than to 'friction with the air' as commonly believed.)

Some that I would add:

"Once something is in orbit it is free from Earth's gravity." Even educated people get tripped up on this one; the internet is rife with people suggesting we just "nudge" the International Space Station into lunar orbit. At a much more basic level of misunderstanding, there is the idea that astronauts are "weightless" because they are far away from the earth.

"There is a high tide on the opposite side of the earth from the moon/sun because the earth 'shields' the ocean from the gravitational pull."

That the PI Team is the best group to design and implement their own data systems, rather than bring in people experienced with IT security, data modeling for reuse by other groups, and other data informatics issues.

Related misconception: that their data is so different from other data that a data system must be designed from the ground up for each new experiment.

I hear from time to time people highly educated and skilled in Physics (unlike those believing that heavy objects fall faster than light ones) making the following claim:

... quantum mechanics indicates that certain physical quantities can take only a countable set of discrete values. Consequently, many current approaches to foundational questions in physics and cosmology advocate novel discrete or 'digital' pictures of nature.

The discrete spectra of some quantum observables do not imply/suggest that nature, in particular spacetime, is fundamentally discrete. The spectrum of a continuous operator acting on Hilbert spaces [which is a topological (vector) space, hence is continuous], often has a discrete part. This has nothing to do with spacetime being discrete. If it will (eventually) turn out to be discrete, it will be for other reasons.

That if an object is moving, there must be a force propelling it in that direction.
Students very commonly think that forces cause objects to have velocity, rather than the fact that forces cause objects to change velocity.

Related to this, it really seems to confuse a lot of intro-level physics students when acceleration and velocity vectors are pointed in opposite directions. One of my standard quizzes when I taught freshman physics was to toss a ball straight up and down in the air, and then hand out a position vs. time plot and ask them to sketch the acceleration and velocity vectors at several key points. (neglecting air resistance). Always gets an interesting mix of answers.
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Tim GoodmanFeb 21 '11 at 17:24

A common misconception is that in a double slit experiment, the electrons or the photons go through both slits at the same time and interfere with themselves.

Nothing of the sort ever happens and that idea doesn’t come from quantum mechanics. It is just meaningless to ask the question (from which slit did the particle pass?) in the context of the particular experiment and even more meaningless to say that it went through both. The particle always passes from the one or the other slit if you setup an experiment that asks the question and in the case that you shoot the particles one at a time you always get one hit on the screen and not an interference of portions of the particle.

I think that the misconception has its roots in the wave analogy of the wave function description of quantum mechanics, where you must have a wave passing from both slits in order to have interference on the other side. Of course that picture doesn’t translate to having a particle passing from both slits, but it only states that there exists interference between the wave functions of the two independent events that translates to a distribution of probability for finding a particle on a particular point on the screen. That is a statement of Born’s interpretation that has been recently tested with a triple slit experiment.

One could ask at this point, “Ok, I get it for the electrons, but light behaves like a wave in everyday experience. What happens in that case?”, and the answer is that light behaves like a wave only when you have a large flux of photons and you can go to the continuous field approximation. It is then that the wave-like properties become apparent both for photons and electrons.

Update3: The Feynman Lectures on Physics vol3: Scattering from a crystal (neutrons).

... Let’s review the physics of this experiment. If we could, in principle, distinguish the alternative final states (even though you do not bother to do so), the total, final probability is obtained by calculating the probability for each state (not the amplitude) and then adding them together. If you cannot distinguish the final states even in principle, then the probability amplitudes must be summed before taking the absolute square to find the actual probability. The thing you should notice particularly is that if you were to try to represent the neutron by a wave alone, you would get the same kind of distribution for the scattering of a down spinning neutron as for an up spinning neutron. You would have to say that the “wave” would come from all the different atoms and interfere just as for the up spinning one with the same amplitude. But we know that this is not the way it works. So as we stated earlier, we must be careful not to attribute too much reality to the waves in space. They are useful for certain problems but not for all.

Actually, what you said is not true. First, electron go through both slits at once (if you want to say something contrary, it's much more about taste or interpretation, that 'fighting with a false belief'). Second, while properties of a single photon are interesting, I would not say it does not behave like a wave (it certainly have many wave-like properties).
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Piotr MigdalNov 20 '10 at 9:56

3

Very strange answer. Actually, it only depends on interpretation whether you think that electron passes through both slits. So this means that it is not a misconception at all. Actually, the most attractive interpretation to me (Feynman's path integral) tells you that the electron travels through all paths and all of them are equally important in determining the final amplitude. In particular, the paths through left and right slits interfere.
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MarekDec 1 '10 at 0:04

2

It seems to me like you are trying to propose ancient preconceptions (like the ones Einstein had) that quantum effects appear just as statistics after letting many electrons through the slits. Well, this is obviously not the case. Every single electron behaves quantum mechanically and travels through all the paths (in path integral view) or is a wave that passes through both slits (in Schroedingerian view).
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MarekDec 1 '10 at 0:08

3

Sorry to step in abruptly, but QM does not tell us ANYTHING about the path of the electron. The ONLY objective, measurable and sustainable thing that QM tells us is the OUTCOME of the MEASUREMENTS. I.e. that electrons will hit the screen in some pattern. All the rest is (non-physical) interpretation and subjective.
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Sklivvz♦Dec 3 '10 at 21:16

1

@Sklivvz: but you are implicitly using one such interpretation yourself. Namely, one that tells you that it's unphysical to ask anything except measurements. You have arbitrarily chosen to make measurement the basis of what is physical (and seems you are not even aware of it). The point is, I can take another interpretation, one that tells me where the electrons went and it also perfectly reproduces all the measurements, so there is no problem with it. It's as valid (and physical) an interpretation as yours is ;-)
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MarekDec 4 '10 at 16:12